Here GADEabG_{ADE}^{ab} denotes the abelianization of GADEG_{ADE} and |GADE|\vert G_{ADE}\vert its cardinality, hence ℤ/|GADE|\mathbb{Z}/{\vert G_{ADE}\vert} the cyclic group whose order is the cardinality of GADEG_{ADE}.

Related concepts

References

Finite subgroups of SO(3)SO(3) and Spin(3)Spin(3)

The classification in Theorem goes back to

Felix Klein, chapter I of Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, 1884, translated as Lectures on the Icosahedron and the Resolution of Equations of Degree Five by George Morrice 1888, online version